I'd like to preface this by stating that I'm by no means a physicist or even a physics student, but recently a sibling of mine had a homework assignment in which they had to calculate the amount of energy needed to heat up a house using a very basic formula given by their teacher.
Because of this I was wondering, if there was any way to calculate precisely the amount of energy required to heat up the amount of air (510 m_3), given that the density of air is different depending on the temperature.
The formula I came up with was this:
The idea being that I'd calculate the energy required to heat the air at x degrees using its density at that specific temperature and summing them all etc.
The specific heat capacity for air seems to be the same from 0 to 20 degrees celcius, hence why I just used 1005 flat for it - http://www.engineeringtoolbox.com/air-properties-d_156.html
So is this correct? Why/why not?
Edit: Forgot to add I used the density formula for air from Wikipedia /Density_of_air (can't post link because of rep)